Path-dependent, shrinking, moving targets and beyond, on generic self-affine sets
Ergodic Theory and Dynamical Systems Seminar
1st October 2020, 2:00 pm – 3:00 pm
Online via Zoom, (if interested, please email one of the organisers to gain access to the Zoom link)
Given a dynamical system (T, X) and a sequence of targets (B_n) of X, the shrinking target problem is a question about the size of the set of points x of X which have infinitely many n such that at time n x hits the target B_n. We calculate the Hausdorff dimension of some shrinking target -type sets on generic self-affine sets. To be more precise, the dynamical system under consideration is the expanding inverse dynamics on a self-affine set with generic translations, and the target sets are moving and shrinking at a speed that depends on the path of x. Further problems of similar flavour and refinements of the dimension result are also explored.
This work is joint with Lingmin Liao and Michal Rams.